Electroosmotic flow (EOF), a phenomenon resulting from the interaction of an external electric field and surface free charges in the electric double layer, is widely used as one major mechanism for fluid transportation in microfluidic devices. As a result, full understanding of EOF in a microchannel is beneficial for guiding the design, operation and analysis of microfluidic systems. Most previous studies on EOF have focused on a flow in a microchannel with smooth walls and uniform surface charges. In some applications, however, the channel geometry varies (thus the electric field alters), and/or the surface charges are non-uniformly distributed; both of them affect EOF. In this work, we investigate one such variation represented by a wavy channel between a plane wall and a sinusoidal wall. We present an analytical solution to the EOF in the wavy channel using complex function theory. The effects of the channel width and wave amplitude on the electric field, streamline pattern, and flow rate are studied. The similarity between the electric field and the EOF velocity is also discussed. In particular, we report our observation of recirculation regions when an adverse pressure gradient is added to an EOF in the wavy channel. Experimental results are presented to validate the theoretical prediction and the analytical solution.